Gell-Mann matrices

Here both, ta and Aa> are the antisymmetric generators of 87/(3), i.e., the antisymmetric Gell-Mann matrices (A, A e 2,5,7 ), acting in flavor and color space, respectively. In the two-flavor color superconducting phase (2SC) where only the light quarks are involved in the condensation, the flavor index in Eq. (1) is restricted to A = 2. In this case it is always possible, without loss of generality, to perform a color rotation such that the 2SC phase is described by s22 / 0 and saa = 0 if (A, A ) (2,2). 

According to Gell-Mann and Low (1951) and Sucher (1957) the energy shift of an unperturbed A-electron state N) can be derived from the S matrix element (up to an irrelevant, state-independent constant)... 

Gell-Mann and Low [23] derived a formula which yields the energy shift due to the interaction (149) in terms of the matrix elements of the operator 5. (0, —00) where S. is the electron operator (108) obtained from I5q(109) with replaced by operator (149). Later Sucher [24] derived a symmetrized version of the energy shift formula, containing the matrix elements of the operator 5y(oo, —00) and which is more suitable for the renormalization procedure. 

This S matrix approach leads to the modified Gell-Mann-Low formula for the energy shift... 

Abstract A consistent relativistic energy approach to the calculation of probabilities of cooperative electron-gamma-nuclear processes is developed. The nuclear excitation by electron transition (NEET) effect is studied. The NEET process probability and cross section are determined within the S-matrix Gell-Mann and Low formalism (energy approach) combined with the relativistic many-body perturbation theory (PT). Summary of the experimental and theoretical works on the NEET effect is presented. The calculation results of the NEET probabilities for the y Os, yy Ir, and yg Au atoms are presented and compared with available experimental and alternative theoretical data. The theoretical and experimental study of the cooperative electron-gamma-nuclear process such as the NEET effect is expected to allow the determination of nuclear transition energies and the study of atomic vacancy effects on nuclear lifetime and population mechanisms of excited nuclear levels. 

Mann, B. K. and West, J. L. 2002. Gell adhesion peptides alter smooth muscle cell adhesion, proliferation, migration, and matrix protein synthesis on modified surfaces and in polymer scaffolds. / Biomed Mater Res 60 86-93. 

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